In order to open a piezoelectrically actuated injection valve for a fuel injection, an electrical control signal is applied to a piezoelectric actuator of the injection valve, whereupon the piezoelectric actuator opens a closing element of the injection valve that is typically embodied as a valve needle. Owing to very fast response characteristics of piezoelectric actuators of said type even very small injection quantities can be metered relatively accurately by means of such injection valves and if necessary a plurality of single injections can be performed in succession in a short time span. However, a manufacturing-related or wear-induced idle stroke between the piezoelectric actuator and the closing element is inevitable and the precise value thereof is generally unknown. Such an idle stroke, which comes about due to play between the piezoelectric actuator and the closing element, leads to a situation where the injection valve does not open following its actuation until after a delay whose length is not precisely known. This in turn leads to a disadvantageous lack of precision in terms of an injection time instant, which shall be defined here as the beginning of a single injection, and also, as a consequence thereof, to a discrepancy between an actually injected fuel quantity and a target injection quantity.